General Relativity with small cosmological constant from spontaneous compactification of Lovelock theory in vacuum

TL;DR

This paper demonstrates that Einstein gravity with a small cosmological constant and extra compact dimensions can emerge from vacuum Lovelock gravity through spontaneous compactification, revealing novel effects on fundamental constants.

Contribution

It shows how four-dimensional Einstein gravity with a small cosmological constant arises from higher-dimensional Lovelock theory with compact extra dimensions, including new effects on gauge and Newton constants.

Findings

Einstein gravity with small cosmological constant derived from Lovelock theory.

Effective four-dimensional constants are shifted relative to higher-dimensional values.

Higher dimensions must be at least seven for this mechanism to work.

Abstract

It is shown that Einstein gravity in four dimensions with small cosmological constant and small extra dimensions can be obtained by spontaneous compactification of Lovelock gravity in vacuum. Assuming that the extra dimensions are compact spaces of constant curvature, General Relativity is recovered within certain class of Lovelock theories possessing necessarily cubic or higher order terms in curvature. This bounds the higher dimension to be at least seven. Remarkably, the effective gauge coupling and Newton constant in four dimensions are not proportional to the gravitational constant in higher dimensions, but shifted with respect to their standard values. This effect opens up new scenarios where a maximally symmetric solution in higher dimensions could decay into the compactified spacetime either by tunneling or through a gravitational analogue of ghost condensation. Indeed, this is what occurs requiring both the extra dimensions and the four-dimensional cosmological constant to be small.